Automated optimization of polymer extrusion dies using finite element analysis

An extrusion die is used to continuously produce parts with a constant cross section; such as sheets, pipes, tire components and more complex shapes such as window seals. The die is fed by a screw extruder when polymers are used. The extruder melts, mixes and pressures the material by the rotation of either a single or double screw. The polymer can then be continuously forced through the die producing a long part in the shape of the die outlet. The extruded section is then cut to the desired length. Generally, the primary target of a well designed die is to produce a uniform outlet velocity without excessively raising the pressure required to extrude the polymer through the die. Other properties such as temperature uniformity and residence time are also important but are not directly considered in this work. Designing dies for optimal outlet velocity variation using simple analytical equations are feasible for basic die geometries or simple channels. Due to the complexity of die geometry and of polymer material properties design of complex dies by analytical methods is difficult. For complex dies iterative methods must be used to optimize dies. An automated iterative method is desired for die optimization. To automate the design and optimization of an extrusion die two issues must be dealt with. The first is how to generate a new mesh for each iteration. In this work, this is approached by modifying a Parasolid file that describes a CAD part. This file is then used in a commercial meshing software. Skewing the initial mesh to produce a new geometry was also employed as a second option. The second issue is an optimization problem with the presence of noise stemming from variations in the mesh and cumulative truncation errors. In this work a simplex method and a modified trust region method were employed for automated optimization of die geometries. For the trust region a discreet derivative and a BFGS Hessian approximation were used. To deal with the noise in the function the trust region method was modified to automatically adjust the discreet derivative step size and the trust region based on changes in noise and function contour. Generally uniformity of velocity at exit of the extrusion die can be improved by increasing resistance across the die but this is limited by the pressure capabilities of the extruder. In optimization, a penalty factor that increases exponentially from the pressure limit is applied. This penalty can be applied in two different ways; the first only to the designs which exceed the pressure limit, the second to both designs above and below the pressure limit. Both of these methods were tested and compared in this work.

SOLUTE-DERIVED THERMAL STABILITY OF NANOCRYSTALLINE ALUMINUM AND PROCESSING FACTOR INFLUENCE ON THE FORMATION OF AL6MN QUASICRYSTALS IN MELT-SPINNING

Thermal stability of nanograined metals can be difficult to attain due to the large driving force for grain growth that arises from the significant boundary area constituted by the nanostructure. Kinetic approaches for stabilization of the nanostructure effective at low homologous temperatures often fail at higher homologous temperatures. Thermodynamic approaches for thermal stabilization may offer higher temperature stability. In this research, modest alloying of aluminum with solute (1 at.% Sc, Yb, or Sr) was examined as a means to thermodynamically stabilize a bulk nanostructure at elevated temperatures. After using melt-spinning and ball-milling to create an extended solid-solution and nanostructure with average grain size on the order of 30-45 nm, 1 h annealing treatments at 673 K (0.72 Tm) , 773 K (0.83 Tm) , and 873 K (0.94 Tm) were applied. The alloys remain nanocrystalline (<100 nm) as measured by Warren-Averbach Fourier analysis of x-ray diffraction peaks and direct observation of TEM dark field micrographs, with the efficacy of stabilization: Sr>Yb>Sc. Disappearance of intermetallic phases in the Sr and Yb alloys in the x-ray diffraction spectra are observed to occur coincident with the stabilization after annealing, suggesting that precipitates dissolve and the boundaries are enriched with solute. Melt-spinning has also been shown to be an effective process to produce a class of ordered, but non-periodic crystals called quasicrystals. However, many of the factors related to the creation of the quasicrystals through melt-spinning are not optimized for specific chemistries and alloy systems. In a related but separate aspect of this research, meltspinning was utilized to create metastable quasicrystalline Al6Mn in an α-Al matrix through rapid solidification of Al-8Mn (by mol) and Al-10Mn (by mol) alloys. Wheel speed of the melt-spinning wheel and orifice diameter of the tube reservoir were varied to determine their effect on the resulting volume proportions of the resultant phases using integrated areas of collected x-ray diffraction spectra. The data were then used to extrapolate parameters for the Al-10Mn alloy which consistently produced Al6Mn quasicrystal with almost complete suppression of the equilibrium Al6Mn orthorhombic phase.